%I #14 May 08 2024 05:13:03
%S 1,5,129,7797,848481,145041093,35799178401,12045448529397,
%T 5298881528389185,2952169020073027845,2031522244065649876545,
%U 1692164698229362361298165,1677876856826199251515980705
%N Expansion of e.g.f. tan(arcsin(arctanh(x))) (odd powers only).
%F a(n) = (2*n+1)!*sum(k=0..n, 16^(-k)*binomial(2*k,k)*(2*k+1)!*sum(i=2*k+1..2*n+1, (2^i*Stirling1(i,2*k+1)*binomial(2*n,i-1))/i!))/2. - _Vladimir Kruchinin_, Jun 17 2011
%e tan(arcsin(arctanh(x))) = x + (5/3!)*x^3 + (129/5)!*x^5 + (7797/7!)*x^7 + (848481/9!)*x^9 + ...
%t With[{nn=30},Take[CoefficientList[Series[Tan[ArcSin[ArcTanh[x]]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, May 08 2024 *)
%o (Maxima)
%o a(n):=(2*n+1)!*sum(16^(-k)*binomial(2*k,k)*(2*k+1)!*sum((2^i*stirling1(i,2*k+1)*binomial(2*n,i-1))/i!,i,2*k+1,2*n+1),k,0,n)/2; /* _Vladimir Kruchinin_, Jun 17 2011 */
%K nonn
%O 1,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)